You can elect COBRA for you and your family if you otherwise would lose coverage because:
The law lets you continue coverage for up to 18 months if you quit, lose a job, or your hours are reduced, and up to three years if the coverage loss was due to other reasons.
In addition, health plan “dependents” (such as spouses and children) can elect COBRA if they lose eligibility for coverage because of:
Keep in mind that you must be covered by the employer-sponsored plan at the time of your job loss or other event, or you aren’t eligible for COBRA.